5.2.4.1 Bivariate Probit Model
In this study the incidence of illness is modelled as a function of the averting behaviour through a bivariate probit model following Alberini et al., 1996). This model assumes a correlation between averting behaviour and presence of illness (and its associated damage costs; see Briscoe et al., 1990). Likewise, the significance of different variables at explaining the presence of averting behaviour and illness is analysed with this model.
A household perceives being unfavourably affected by contamination when illness occurs and deems averting behaviour necessary. The incidence of illness is a function of the level of contamination and the household's averting behaviour. Contamination is exogenous to the household but averting behaviour is endogenous. So, this model assumes observed independent variables and unobserved risk factors, e.g. daily fluctuations in drinking water quality. Such a model captures the effect of behaviour on health and is therefore useful for analysing real-world situations, since it treats health and behaviour as interlinked variables (Alberini et al., 1996; Dasgupta, 2004; Fleming and Kler, 2008).
Furthermore, this model is based on respondents’ water quality perceptions, employing a discrete yes or no according if they thought their water was contaminated or not; instead of the measure of actual contamination levels which are unavailable for the study site (see Um et al., 2002). Following is the formula for
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the bivariate probit model used and formed by two binary choice models nested together
𝑦1∗ = 𝑥
1𝛽1+ 𝛾1𝑅∗+ 𝜀 𝑦2∗ = 𝑥
2𝛽2 + 𝛾2𝑅∗+ 𝛿𝑦1∗ + 𝑣
Presence of averting behaviour is represented by 𝑦1∗ and presence of illness by 𝑦2∗. Presence of averting behaviour 𝑦1∗ is determined by individual and household characteristics (e.g. monthly income, water bill) and proxies for risk factors known to the researcher (e.g. type of toilet available) 𝑥1 and unknown risk factors 𝑅∗ (e.g. fluctuations in water quality). Presence of illness 𝑦2∗ depends on 𝑥2 , 𝑅∗ and whether a household carries out averting behaviours 𝑦1∗ or not. There are three parameters of interest to be estimated: 𝛽, 𝛾, and 𝛿. While 𝜀 and 𝑣 represent normally distributed error terms with mean zero, variance one and correlation 𝜌. These two error terms are jointly distributed, but are assumed to be independent of each other, and capture the unobserved determinants of presence of illness and presence of averting behaviour, respectively. Because the risk factor 𝑅∗ is not known to the researcher, it is absorbed into the error terms. In this analysis, the independent variables of individual and household characteristics 𝑥1 were selected based on the literature and any variables exhibiting significant Pearson correlations above 0.4 were excluded from the model to avoid multi-collinearity. The independent variables included in the bivariate model are described in Table 5.1, as well as the expected sign for the model.
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Table 5.1. Independent variables included in the bivariate probit model for the presence of averting behaviour and illness. Note: the classification of stable and temporal jobs is explained in Appendix 12.
Variable Expected sign AB
Expected
sign illness Explanation
Age in years ? ? Expected to be significant, but no a priori reason Continues… Education
above primary school
+ - Education likely to increase desire for improved water quality
At least one child under 15 years
+ - Children’s health is a family concern and clean drinking water is provided to them
Has toilet or latrine
+ - Having a toilet or latrine is a sign of sanitary awareness
Stable job + - A stable job is likely linked to higher income and education Partner has
stable job
+ - A stable job is likely linked to higher income and education Large
community
+ - Larger communities have higher levels of income and education Group member + - Being in groups facilitates social and environmental awareness
Has car + - Richer individuals have greater
access to averting methods Cable television + - Richer individuals with access to
social media have access to averting behaviour methods to reduce illness
Household income above minimum wage
+ - Richer individuals have access to averting methods to reduce illness
2 60 Variable Expected sign AB Expected
sign illness Explanation
Water bill - - Those paying a high water bill
might expect clean water Drinks from
piped water system
- - The piped system is expected to provide cleaner water than other sources
Water quality perception
+ + Thinking water is contaminated is one of the main reasons for presence of illness and thus averting
Water interruptions
+ + Water interruptions are linked to water contamination and illness
5.2.4.2 Averting Expenditure Estimates
The three averting expenditure estimates (labourer, national minimum wage and market) were calculated by first estimating probit models with independent variables and subsequently welfare measures using Nlogit - Limdep 4.0 software (same as for the CV probit model, see detailed information on procedure in section 4.2.5 of chapter 4). Although the significance of the independent variables is not discussed, they are employed to obtain a realistic WTP considering the effect of these variables on respondents’ preferences.
The consumption of bottled water has risen in the last decade worldwide not only because it is being perceived as a source of potable water, but also as water of good taste, odour and appearance (e.g. Doria, 2006; Ward et al., 2009; Hu et al., 2011; Saylor et al., 2011). These multiple benefits of bottled water are referred to as joint production, which is an important limitation of averting behaviour. Joint production is more likely to exist in studying long-term or persistent drinking water contamination situations (Abdalla et al., 1992), as is the case at the study site. Bottled water has also become a popular market commodity, a form of cultural
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consumption driven by status competition or as a lifestyle choice (Wilk, 2006; York et al., 2011). This status-derived benefit contributes to jointness but it is believed that this is not as great as its utilitarian value as a source of potable water (Knox and de Chernatony, 1989). Thus, to account for the jointness of bottled water at the study site, averting expenditure on bottled water is reduced by a conservative 11%, considering that the study site is a poor rural setting. This proportion is an average of Abrahams et al., 2000) findings of bottled water jointness in Georgia, USA.
5.2.4.3 Illness Damage Cost Estimate
As described in the previous section, data were collected on the damage costs for the six months before and up to the survey application. This six month value was converted to a weighted monthly value using secondary data from the government. However, it is recognised that the symptoms surveyed might be due to other non- water related causes as evidenced by some high outlier values. In order to account for this, 3% is trimmed off at both ends of the initial estimates as a valid method of removing outliers (e.g. Ramsey and Ramsey, 2007). Estimates were calculated based on all symptoms and for diarrhoea only cases, so that a broad value and a more conservative value were obtained.
Common problems with the data from revealed preference methods, such as averting behaviour and damage costs, are recall bias and incomplete information. Recall bias arises when people are asked to recall expenditures over a long time period (Chu et al., 1992); and incomplete information can occur when people do not have full information when they make purchase decisions (Boyle, 2003b). These limitations are considered when analysing the results and by referring to them as conservative estimates. Finally, the revealed WTP was calculated by summing the averting expenditure estimate and the damage cost estimate.
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5.3 Results